I had a Nikon 105 2.8 VR (the first version), sharp lens but the autofocus hunted REALLY badly.

I now use an older Nikon AI-S F/2.5 manual focus lens (you don't really need auto focus for Macro anyway), I picked it up in great condition for $125 on The Bay.

One of the FEW off-brand lenses I ever recommend is the Tokina 100mm f/2.8 but it won't autofocus on your 5200 either... IMHO 100 is as short as you want to go for bugs... anything shorter than that and you get into issues of getting too close to the critters.

Dedicated Macro lens for insect, I recommend getting one with at least 90mm focal length. Most of them are pretty good and close in terms of optical quality. It all comes down to additional features, cost and condition if buy used.

- The newer one have IS/VR/VC/OS to stabilize the image. It help for handheld shots but it increase cost.
- Some of them use internal focus system so that the lens won't extend when shoot at 1:1 ratio. The min. focus of the lens is the distance from the subject to the focal plane (which is either the sensor or film), so when the lens is extended (to shoot at 1:1 ratio), the front element of the lens will be closer to the subject. But that is not the case with some lens with internal focus system. However, those have the internal focus system usually cost more.
- Build quality of the lens may also affect the cost. However, most of them are on the good build quality side especially the higher price one or some of the old lens. There is one non-production macro lens made by Cosina (1:2 ratio but comes with a dioptor too make it 1:1) were made of cheap plastic, but not bad at all as far as optical goes.

If I were you, I will first determine the budget and then find a macro lens that fit that budget. The price range vary from $100 to over $1000.

I have the 60mm f/2.8G macro. Works good on the crop body (like a D5200). I've gotten many insects, they generally are not bothered by a lens in their face. Flying insects will usually stay around if I move in very slowly. It is also small enough that I never have to think, take the lens or leave it.

I like to use a tripod with macro, but still pending a gear head and probably a focusing rail. Off camera flash is often helpful. The tilt screen on the D5200 will help, I often find it hard to look through the viewfinder with some positions the camera ends up in (tethered shooting works good indoors, but have broken too many things outdoors to do that in the field).